Related papers: Quantum geometry in condensed matter
Quantum mechanics is among the most important and successful mathematical model for describing our physical reality. The traditional formulation of quantum mechanics is linear and algebraic. In contrast classical mechanics is a geometrical…
Recently, it has been shown that a quantum system held in spatial superposition and then eventually recombined does experience decoherence from black hole horizons, at a level increasing linearly with the time the superposition has been…
Momentum space of a gapped quantum system is a metric space: it admits a notion of distance reflecting properties of its quantum ground state. By using this quantum metric, we investigate geometric properties of momentum space. In…
The optical selection rules dictate symmetry-allowed/forbidden transitions, playing a decisive role in engineering exciton quantum states and designing optoelectronic devices. While both the real (quantum metric) and imaginary (Berry…
Quantum geometry is a key quantity that distinguishes electrons in a crystal from those in the vacuum. Its study continues to provide insights into quantum materials, uncovering new design principles for their discovery. However, unlike the…
The discovery of the quantum Hall effect founded the field of topological condensed matter physics. Its amazingly accurate quantisation of the Hall conductance, now enshrined in quantum metrology, is topologically protected: it is stable…
Non-zero curvature in a waveguide leads to the appearance of an attractive quantum potential which crucially affects the dynamics in matter-wave circuits. Using methods of supersymmetric quantum mechanics, pairs of bent waveguides are found…
Quantum metric and Berry curvature are the real part and imaginary part of the quantum geometric tensor, respectively. The T-odd (T: time-reversal) nonlinear Hall effect driven by the quantum metric dipole, recently confirmed in Science…
A simple mapping procedure is presented by which classical orbits and path integrals for the motion of a point particle in flat space can be transformed directly into those in curved space with torsion. Our procedure evolved from…
We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…
The experimental observation of the long-sought quantum anomalous Hall effect was recently reported in magnetically doped topological insulator thin films [Chang et al., Science 340, 167 (2013)]. An intriguing observation is a rapid…
The integral and fractional quantum Hall effects are among the most important discoveries in condensed matter physics in 1980s. The main results can be summarized in the conductance matrix. When the filling factor is an integer or some…
Canonical quantum gravity provides insights into the quantum dynamics as well as quantum geometry of space-time by its implications for constraints. Loop quantum gravity in particular requires specific corrections due to its quantization…
We review the main features of a mathematical framework encompassing some of the salient quantum mechanical and geometrical aspects of Hall systems with finite size and general boundary conditions. Geometrical as well as algebraic…
We introduce the concept of quantum weight as a ground state property of quantum many-body systems that is encoded in the static structure factor and characterizes density fluctuation at long wavelengths. The quantum weight carries a wealth…
The change of the effective dimension of spacetime with the probed scale is a universal phenomenon shared by independent models of quantum gravity. Using tools of probability theory and multifractal geometry, we show how dimensional flow is…
The so-called quantum metric tensor is a band-structure invariant whose measure corresponds to the quantum distance between nearby states in the Hilbert space, characterizing the geometry of the underlying quantum states. In the context of…
I propose a quantum gravity model in which geometric space emerges from random bits in a quantum phase transition driven by the combinatorial Ollivier-Ricci curvature and corresponding to the condensation of short cycles in random graphs.…
We present a general unified approach for the study of quantum thermal machines, including both heat engines and refrigerators, operating under periodic adiabatic driving and in contact with thermal reservoirs kept at different…
Geometric quantum mechanics aims to express the physical properties of quantum systems in terms of geometrical features preferentially selected in the space of pure states. Geometric characterisations are given here for systems of one, two,…